filename stringlengths 5 42 | content stringlengths 15 319k |
|---|---|
Fin.lean | /-
Copyright (c) 2021 Ivan Sadofschi Costa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ivan Sadofschi Costa
-/
import Mathlib.Data.Finsupp.Single
/-!
# `cons` and `tail` for maps `Fin n →₀ M`
We interpret maps `Fin n →₀ M` as `n`-tuples of elements of `M`,
We def... |
AesopUnusedTactic.lean | /-
Copyright (c) 2024 Jannis Limperg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jannis Limperg
-/
import Aesop
import Mathlib.Tactic.Linter.UnusedTactic
set_option linter.unusedTactic true
/-
The unused tactic linter should not consider tactics unused if they a... |
Periodic.lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Alex Kontorovich, Heather Macbeth
-/
import Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar
import Mathlib.MeasureTheory.Measure.Haar.Quotient
import Mathlib.MeasureThe... |
Imo2013Q1.lean | /-
Copyright (c) 2021 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib.Algebra.BigOperators.Group.Finset.Powerset
import Mathlib.Algebra.Order.Field.Rat
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Positivity.Basic
... |
IsGaloisGroup.lean | /-
Copyright (c) 2025 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.FieldTheory.Galois.Basic
import Mathlib.RingTheory.Invariant.Defs
/-!
# Predicate for Galois Groups
Given an action of a group `G` on an extension ... |
Module.lean | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic
import Mathlib.Algebra.Category.AlgCat.Basic
import Mathlib.CategoryTheory.Monoidal.Mon_
/-!
# `Mon_ (ModuleCat ... |
Basic.lean | /-
Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1
/-! # Conditional expectation
We build the conditional expectation of an integrable function `f` ... |
Opposite.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.Algebra.Field.Defs
import Mathlib.Algebra.Ring.Opposite
import Mathlib.Data.Int.Cast.Lemmas
/-!
# Field structure on the multiplicative/additive opposite
-/
as... |
Module.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kenny Lau
-/
import Mathlib.Algebra.GroupWithZero.Action.Pi
import Mathlib.Algebra.Module.LinearMap.Defs
import Mathlib.Algebra.Module.Pi
import Mathlib.Data.DFinsupp.Defs
... |
GroupCompletion.lean | /-
Copyright (c) 2024 Mitchell Lee. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitchell Lee
-/
import Mathlib.Topology.Algebra.GroupCompletion
import Mathlib.Topology.Algebra.InfiniteSum.Group
/-!
# Infinite sums in the completion of a topological group
-/
open U... |
congrm.lean | import Mathlib.Algebra.Ring.Nat
import Mathlib.Data.Fintype.Card
import Mathlib.Tactic.CongrM
private axiom test_sorry : ∀ {α}, α
namespace Tests.Congrm
set_option autoImplicit true
section docs
/-! These are the examples from the tactic documentation -/
example {a b c d : ℕ} :
Nat.pred a.succ * (d + (c + a.pr... |
Relations.lean | /-
Copyright (c) 2025 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic
import Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Lemmas
import Mathlib.Algebra.Lie.Sl2
/-!
# Relatio... |
Basic.lean | /-
Copyright (c) 2021 Luke Kershaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Luke Kershaw
-/
import Mathlib.CategoryTheory.Adjunction.Limits
import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products
import Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproduct... |
Maps.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.Data.DFinsupp.Module
import Mathlib.RingTheory.Ideal.Operations
/-!
# Maps on modules and ideals
Main definitions include `Ideal.map`, `Ideal.comap`, `RingHom.... |
Topology.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction
import Mathlib.Analysis.Convex.Contractible
import Mathlib.Analysis.LocallyConvex.WithSeminorms
import ... |
order.lean | import Mathlib.Data.Matrix.Rank
import Mathlib.Tactic.Order
example (a b c : Nat) (h1 : a ≤ b) (h2 : b ≤ c) : a ≤ c := by
order
example (a b c d e : Nat) (h1 : a ≤ b) (h2 : b ≤ c) (h3 : c ≤ d) (h4 : d ≤ e) (h5 : b ≠ d) :
a < e := by
order
example (a b c : Nat) (h1 : a = b) (h2 : b = c) : a = c := by
order
... |
Basic.lean | /-
Copyright (c) 2018 Michael Jendrusch. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Jendrusch, Kim Morrison
-/
import Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
import Mathlib.CategoryTheory.Monoidal.Functor
import Mathlib.CategoryTheory.Limits.Types.S... |
vector.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype bigop fi... |
cyclotomic.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path.
From mathcomp Require Import div choice fintype tuple finfun bigop prime.
From mat... |
PullbackCone.lean | /-
Copyright (c) 2018 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Markus Himmel, Bhavik Mehta, Andrew Yang, Emily Riehl, Calle Sönne
-/
import Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan
/-!
# PullbackCone
This file provides AP... |
Basic.lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Group.Embedding
import Mathlib.Algebra.Order.Interval.Set.Monoid
import Mathlib.Order.Interval.Finset.Defs
/-!
# Algebraic properties of finset in... |
cyclotomic.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path.
From mathcomp Require Import div choice fintype tuple finfun bigop prime.
From mat... |
MonotoneContinuity.lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Heather Macbeth
-/
import Mathlib.Topology.Homeomorph.Defs
import Mathlib.Topology.Order.LeftRightNhds
/-!
# Continuity of monotone functions
In this file we prove ... |
SMul.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Alexander Bentkamp
-/
import Mathlib.Algebra.Algebra.Defs
import Mathlib.LinearAlgebra.Basis.Basic
/-!
# Bases and scalar multiplication
This file def... |
MinMax.lean | /-
Copyright (c) 2019 Minchao Wu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Minchao Wu, Chris Hughes, Mantas Bakšys
-/
import Mathlib.Data.List.Basic
import Mathlib.Order.BoundedOrder.Lattice
import Mathlib.Data.List.Induction
import Mathlib.Order.MinMax
import Ma... |
Countable.lean | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
import Mathlib.CategoryTheory.EssentiallySmall
import Mathlib.CategoryTheory.FinCategory.Basic
import Mathlib.Data.Fintype.EquivFin
import Mathlib.Data.Countable.... |
TermCongr2.lean | import Mathlib.Tactic.TermCongr
import Mathlib.Data.Fintype.Card
import Mathlib.Tactic.Ring
/-!
`congr(...)` tests with heavier imports (`TermCongr` is in `Mathlib/Tactic/Common.lean`)
-/
namespace Tests
set_option autoImplicit true
-- set_option trace.Elab.congr true
example [Fintype α] [Fintype β] (h : α = β) : ... |
SuppressCompilation.lean | /-
Copyright (c) 2023 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex J. Best, Mac Malone
-/
import Mathlib.Init
import Lean.Elab.Declaration
import Lean.Elab.Notation
/-!
# Suppressing compilation to executable code in a file or in a section
C... |
Defs.lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Sébastien Gouëzel, Zhouhang Zhou, Reid Barton
-/
import Mathlib.Topology.ContinuousMap.Defs
import Mathlib.Topology.Maps.Basic
/-!
# Homeomorphisms
This ... |
Basic.lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johan Commelin
-/
import Mathlib.Algebra.Group.Basic
import Mathlib.Algebra.Group.Equiv.Defs
import Mathlib.Algebra.Group.WithOne.Defs
/-!
# More operations on `WithOn... |
Coherence.lean | /-
Copyright (c) 2021 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import Mathlib.CategoryTheory.Monoidal.Free.Basic
import Mathlib.CategoryTheory.Discrete.Basic
/-!
# The monoidal coherence theorem
In this file, we prove the monoida... |
CompactlyGenerated.lean | /-
Copyright (c) 2024 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker, Etienne Marion
-/
import Mathlib.Topology.Compactness.CompactlyGeneratedSpace
import Mathlib.Topology.Maps.Proper.Basic
/-!
# A map is proper iff preimage of compa... |
interval.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import div fintype bigo... |
NumDen.lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
-/
import Mathlib.RingTheory.Localization.FractionRing
import Mathlib.RingTheory.Localization.Integer
import Mathli... |
BaseChange.lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.LinearAlgebra.QuadraticForm.TensorProduct
import Mathlib.LinearAlgebra.CliffordAlgebra.Conjugation
import Mathlib.LinearAlgebra.TensorProduct.Opposite
import... |
FundamentalTheorem.lean | /-
Copyright (c) 2023 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
import Mathlib.RingTheory.MvPolynomial.Symmetric.Defs
import Mathlib.RingTheory.MvPolynomial.Tower
import Mathlib.Data.Finsupp.Notation
import Mathlib.Data.Finsupp.WellFounded
... |
interval.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import div fintype bigo... |
Basic.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kim Morrison
-/
import Mathlib.Algebra.BigOperators.Finsupp.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Preimage
import Mathlib.Algebra.Group.Indicator
impor... |
ssrmatching.v | From Corelib Require Export ssrmatching.
|
algC.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun ssrnat eqtype seq choice.
From mathcomp Require Import div fintype path... |
presentation.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq.
From mathcomp Require Import fintype finset fingroup morphism.
(**********************... |
gseries.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path.
From mathcomp Require Import fintype bigop finset fingroup morphism.
From mathcomp... |
CodiscreteCategory.lean | /-
Copyright (c) 2024 Alvaro Belmonte. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alvaro Belmonte, Joël Riou
-/
import Mathlib.CategoryTheory.EqToHom
import Mathlib.CategoryTheory.Pi.Basic
import Mathlib.Data.ULift
import Mathlib.CategoryTheory.Category.Cat
import ... |
MixedCharZero.lean | /-
Copyright (c) 2022 Jon Eugster. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jon Eugster
-/
import Mathlib.Algebra.CharP.LocalRing
import Mathlib.RingTheory.Ideal.Quotient.Basic
import Mathlib.Tactic.FieldSimp
/-!
# Equal and mixed characteristic
In commutative ... |
Monotone.lean | /-
Copyright (c) 2014 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Andrew Zipperer, Haitao Zhang, Minchao Wu, Yury Kudryashov
-/
import Mathlib.Data.Set.Function
/-!
# Monotone functions over sets
-/
variable {α β γ : Type*}
open Equi... |
Operations.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Yury Kudryashov
-/
import Mathlib.Data.ENNReal.Real
/-!
# Properties of addition, multiplication and subtraction on extended non-negative real numbers
In this file we... |
ssrmatching.v | From Corelib Require Export ssrmatching.
|
CategoryTheory.lean | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import Mathlib.RingTheory.Flat.Basic
import Mathlib.Algebra.Homology.ShortComplex.ModuleCat
import Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic
/-!
# Tensoring with... |
Filter.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Order.Filter.Cofinite
/-!
# Computational realization of filters (experimental)
This file provides infrastructure to compute with filters.
## Main d... |
HalesJewett.lean | /-
Copyright (c) 2021 David Wärn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wärn
-/
import Mathlib.Data.Fintype.Option
import Mathlib.Data.Fintype.Shrink
import Mathlib.Data.Fintype.Sum
import Mathlib.Data.Finite.Prod
import Mathlib.Algebra.BigOperators.Grou... |
Operations.lean | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Jireh Loreaux, Yunzhou Xie
-/
import Mathlib.Algebra.Group.Subgroup.Map
import Mathlib.Algebra.Module.Opposite
import Mathlib.Algebra.Module.Submodule.Lattice
import Mathli... |
test_guard.v | From mathcomp Require Import all_boot.
Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
Inductive tree := Node { children : seq tree }.
Inductive ptree (T : Type) := singleton of T | branch of list (ptree T).
(* has *)
Fixpoint tree_has (T : Type) (p : pred T) (t : ptree T) : bool :... |
Split.lean | import Mathlib.Tactic.Basic
example : (α : Type) × List α := by
constructor
· exact [0,1]
-- example : (α : Type) × List α := by
-- fsplit
-- - exact ℕ
-- - exact [0,1]
|
ShortExact.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Algebra.Homology.HomotopyCategory.ShortExact
import Mathlib.Algebra.Homology.DerivedCategory.Basic
/-!
# The distinguished triangle attached to a short exact se... |
Field.lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import Mathlib.Algebra.Ring.Action.Basic
import Mathlib.Algebra.Field.Defs
import Mathlib.Algebra.GroupWithZero.Units.Lemmas
/-!
# Group action on fields
-/
variable {M} [Mon... |
Rat.lean | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro
-/
import Mathlib.Algebra.Field.Defs
import Mathlib.Data.NNRat.Defs
/-!
# The rational numbers form a field
This file contains the field instance on th... |
ClearExcept.lean | import Mathlib.Tactic.ClearExcept
set_option linter.unusedTactic false
set_option linter.unusedVariables false
-- Most basic test
example (_delete_this : Nat) (dont_delete_this : Int) : Nat := by
clear * - dont_delete_this
fail_if_success assumption
exact dont_delete_this.toNat
-- Confirms that clearExcept doe... |
sesquilinear.v | From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq div.
From mathcomp Require Import choice fintype tuple bigop ssralg finset fingroup.
From mathcomp Require Import zmodp poly order ssrnum matrix mxalgebra vector.
(************************************************... |
Closure.lean | /-
Copyright (c) 2024 Peter Nelson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Peter Nelson
-/
import Mathlib.Data.Matroid.Map
import Mathlib.Order.Closure
import Mathlib.Order.CompleteLatticeIntervals
/-!
# Matroid Closure
A flat (`IsFlat`) of a matroid `M` is a... |
Constructions.lean | /-
Copyright (c) 2024 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Analysis.CStarAlgebra.Module.Defs
import Mathlib.Analysis.CStarAlgebra.Module.Synonym
import Mathlib.Topology.MetricSpace.Bilipschitz
/-! # Construction... |
Periodic.lean | /-
Copyright (c) 2021 Benjamin Davidson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Benjamin Davidson
-/
import Mathlib.Algebra.Ring.NegOnePow
/-!
# Periodicity
In this file we define and then prove facts about periodic and antiperiodic functions.
## Main defini... |
ValMinAbs.lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.Data.ZMod.Basic
import Mathlib.Tactic.Linarith
/-!
# Absolute value in `ZMod n`
-/
namespace ZMod
variable {n : ℕ} {a : ZMod n}
/-- Returns the integer ... |
Basic.lean | /-
Copyright (c) 2021 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
import Mathlib.LinearAlgebra.FreeModule.Basic
import Mathlib.LinearAlgebra.Matrix.StdBasis
import Mathlib.RingTheory.Finiteness.Cardinality
/-!
# Finite and free m... |
choice.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq.
(**************************************************... |
Order.lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import Mathlib.Algebra.Order.Archimedean.Basic
import Mathlib.Algebra.Order.BigOperators.Ring.Finset
import Mathlib.Topology.Algebra.InfiniteSum.NatInt
import Mathlib... |
Bits.lean | /-
Copyright (c) 2022 Praneeth Kolichala. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Praneeth Kolichala
-/
import Mathlib.Data.Nat.Basic
import Mathlib.Data.Nat.BinaryRec
import Mathlib.Data.List.Defs
import Mathlib.Tactic.Convert
import Mathlib.Tactic.GeneralizePr... |
EpiMono.lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Kim Morrison
-/
import Mathlib.CategoryTheory.Opposites
import Mathlib.CategoryTheory.Groupoid
/-!
# Facts about epimorphisms and monomorphisms.
The definitions of `Epi` an... |
Defs.lean | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.NoZeroSMulDivisors.Basic
import Mathlib.Algebra.Order.GroupWithZero.Action.Synonym
import Mathlib.Algebra.Order.Monoid.Unbundled.Pow
import Mathlib... |
Set.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Group.Action.Pointwise.Set.Basic
import Mathlib.Algebra.GroupWithZero.Action.Basic
import Mathlib.Algebra.GroupWithZero.Action.Units
import Mathlib... |
ULift.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.Topology.Category.TopCat.Basic
import Mathlib.Topology.Homeomorph.Lemmas
/-!
# Lifting topological spaces to a higher universe
In this file, we construct the f... |
Summable.lean | /-
Copyright (c) 2024 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
import Mathlib.Analysis.SpecialFunctions.Complex.LogBounds
/-!
# Summability of logarithms
We give conditions under which the logarithms of a summble sequence is s... |
ZMod.lean | /-
Copyright (c) 2025 Paul Lezeau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Lezeau, Oliver Nash, Yaël Dillies
-/
import Mathlib.Order.Circular
import Mathlib.Order.Fin.Basic
import Mathlib.Data.ZMod.Defs
/-!
# The circular order on `ZMod n`
This file defin... |
BilinearForm.lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Kexing Ying
-/
import Mathlib.LinearAlgebra.BilinearForm.Properties
import Mathlib.LinearAlgebra.Matrix.SesquilinearForm
/-!
# Bilinear form
This file defines the conversio... |
NonLocalRing.lean | /-
Copyright (c) 2025 Michal Staromiejski. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michal Staromiejski
-/
import Mathlib.Algebra.Ring.Pi
import Mathlib.Algebra.Ring.Prod
import Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic
import Mathlib.RingTheory.Spectrum.Ma... |
BoundedLinearMaps.lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
import Mathlib.Analysis.NormedSpace.Multilinear.Basic
import Mathlib.Analysis.Normed.Ring.Units
import Mathlib.Analysis.NormedSpace.OperatorNorm.Mul
... |
order.v | (* (c) Copyright 2006-2019 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq.
From mathcomp Require Import path fintype tup... |
LeastGreatest.lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Mario Carneiro
-/
import Mathlib.Algebra.Order.Group.OrderIso
import Mathlib.Algebra.Ring.Int.Defs
import Mathlib.Data.Nat.Find
import Mathlib.Order.Bounds.Defs
/-! # Le... |
ToMulBot.lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl
-/
import Mathlib.Algebra.Order.GroupWithZero.Canonical
import Mathlib.Algebra.Order.Monoid.Unbundled.TypeTags
import Ma... |
Defs.lean | /-
Copyright (c) 2020 Ashvni Narayanan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ashvni Narayanan
-/
import Mathlib.Algebra.Ring.Subsemiring.Defs
import Mathlib.RingTheory.NonUnitalSubring.Defs
/-!
# Subrings
Let `R` be a ring. This file defines the "bundled" s... |
Basic.lean | /-
Copyright (c) 2019 Kevin Kappelmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin Kappelmann
-/
import Mathlib.Data.Seq.Seq
import Mathlib.Algebra.Field.Defs
/-!
# Basic Definitions/Theorems for Continued Fractions
## Summary
We define generalised, simple... |
Center.lean | /-
Copyright (c) 2020 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
import Mathlib.Algebra.GroupWithZero.Units.Basic
import Mathlib.GroupTheory.Subgroup.Center
/-!
# The center of a group with zero
-/
assert_not_exists Ring
/-- For a gro... |
Discharger.lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, David Renshaw
-/
import Mathlib.Tactic.Positivity.Core
import Mathlib.Util.DischargerAsTactic
/-!
# Discharger for `field_simp` tactic
The `field_simp` tactic ... |
PiTensorProduct.lean | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang
-/
import Mathlib.LinearAlgebra.PiTensorProduct
import Mathlib.Algebra.Algebra.Bilinear
import Mathlib.Algebra.Algebra.Equiv
import Mathlib.Data.Finset.NoncommProd
/-!
# T... |
AssertNoSorry.lean | /-
Copyright (c) 2023 David Renshaw. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Renshaw
-/
import Mathlib.Init
import Lean.Util.CollectAxioms
import Lean.Elab.Command
/-!
# Defines the `assert_no_sorry` command.
Throws an error if the given identifier uses... |
Defs.lean | /-
Copyright (c) 2020 Hanting Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hanting Zhang, Johan Commelin
-/
import Mathlib.Algebra.Algebra.Subalgebra.Basic
import Mathlib.Algebra.MvPolynomial.CommRing
import Mathlib.Combinatorics.Enumerative.Partition
/-!
# S... |
test_intro_rw.v | From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat.
Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
Lemma test_dup1 : forall n : nat, odd n.
Proof. move=> /[dup] m n; suff: odd n by []. Abort.
Lemma test_dup2 : let n := 1 in False.
Proof. move=> /[dup] m n; have : m = n :=... |
Stalks.lean | /-
Copyright (c) 2019 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison, Justus Springer
-/
import Mathlib.Topology.Category.TopCat.OpenNhds
import Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing
/-!
# Stalks
For a presheaf `F` on a topol... |
Biproducts.lean | /-
Copyright (c) 2020 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
import Mathlib.Algebra.Group.Pi.Lemmas
import Mathlib.Algebra.Category.Grp.Preadditive
import Mathlib.CategoryTheory.Preadditive.Biproducts
import Mathlib.Algebra.Categor... |
Sigma.lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Yaël Dillies, Bhavik Mehta
-/
import Mathlib.Data.Finset.Lattice.Fold
import Mathlib.Data.Set.Sigma
import Mathlib.Order.CompleteLattice.Finset
/-!
# Finite sets in a ... |
countalg.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
From mathcomp Require Import fintype bigop ss... |
Superscript.lean | /-
Copyright (c) 2023 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import Mathlib.Init
import Batteries.Tactic.Lint
/-!
# A parser for superscripts and subscripts
This is intended for use in local notations. Basic usage is:
```
loc... |
Submodule.lean | /-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Algebra.Lie.Subalgebra
import Mathlib.LinearAlgebra.Finsupp.Span
/-!
# Lie submodules of a Lie algebra
In this file we define Lie submodules, we construct ... |
Resolution.lean | /-
Copyright (c) 2024 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import Mathlib.CategoryTheory.Localization.LocalizerMorphism
/-!
# Resolutions for a morphism of localizers
Given a morphism of localizers `Φ : LocalizerMorphism W₁ W₂` (i.e.... |
ReflQuiv.lean | /-
Copyright (c) 2024 Mario Carneiro and Emily Riehl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Emily Riehl
-/
import Mathlib.Combinatorics.Quiver.ReflQuiver
import Mathlib.CategoryTheory.Category.Cat
import Mathlib.CategoryTheory.Category.Quiv
/-... |
all_solvable.v | From mathcomp Require Export abelian.
From mathcomp Require Export alt.
From mathcomp Require Export burnside_app.
From mathcomp Require Export center.
From mathcomp Require Export commutator.
From mathcomp Require Export cyclic.
From mathcomp Require Export extraspecial.
From mathcomp Require Export extremal.
From mat... |
bigop.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From HB Require Import structures.
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path.
From mathcomp Require Import div fintype tuple ... |
Finset.lean | /-
Copyright (c) 2022 Eric Wieser, Yaël Dillies, Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Yaël Dillies, Andrew Yang
-/
import Mathlib.Algebra.Order.Ring.Canonical
import Mathlib.Data.Finset.Lattice.Fold
import Mathlib.Data.Nat.Cast.Order... |
automorphism.v | (* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
(* Distributed under the terms of CeCILL-B. *)
From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat fintype.
From mathcomp Require Import finset fingroup perm morphism.
(*********************... |
Exponential.lean | /-
Copyright (c) 2021 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker, Eric Wieser
-/
import Mathlib.Algebra.Ring.Action.ConjAct
import Mathlib.Analysis.Analytic.ChangeOrigin
import Mathlib.Analysis.Complex.Basic
import Mathlib.Data.Na... |
PrimesCongruentOne.lean | /-
Copyright (c) 2020 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
import Mathlib.RingTheory.Polynomial.Cyclotomic.Eval
/-!
# Primes congruent to one
We prove that, for any positive `k : ℕ`, there are infinitely many primes `p` s... |
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